A sequential algorithm of inverse heat conduction problems using singular value decomposition

Cabeza, José María Gutiérrez; García, Juan Andrés Martín; Rodríguez, Ana Ruiz

doi:10.1016/j.ijthermalsci.2004.06.009

Cited by 49 publications

(14 citation statements)

References 22 publications

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“…The authors use an integral equation method and a linear least-squares method. The sequential function specification method supported by singular value decomposition was discussed in [Cabeza et al 2005]. In [Shidfar and Pourgholi 2006;Pourgholi et al 2009], the ill-posed IHCP is transformed to Cauchy's problem by means of a linear transformation.…”

Section: ]{T (T)} + [B]{t (T)} (1-3)mentioning

confidence: 99%

“…The numerical approach combining the use of the finite difference method with the solution of ordinary differential equations has been proposed in [Ebrahimian et al 2007] for solving the 1-D IHCP. The least-squares method has been used to determine the unknown boundary condition [Cabeza et al 2005]. Four different versions of the variable metric method for solving the 1-D IHCP [Luksan and Spedicato 2000] with a symmetric rank-one update are compared in [Pourshaghaghy et al 2007].…”

Section: ]{T (T)} + [B]{t (T)} (1-3)mentioning

confidence: 99%

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Analytical-numerical solution of the inverse problem for the heat conduction equation

Ciałkowski

Maćkiewicz

Kołodziej

et al. 2012

J. Mech. Mater. Struct.

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The solution of the inverse problem for the transient heat transfer equation is considered. The partial differential equation was discretized with respect to the space variable, and a system of ordinary differential equations of first order was obtained. The solution of the system of equations has a wave form. The numerical results obtained from the solution of the inverse problem confirm the effectiveness of the proposed method.

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Section: ]{T (T)} + [B]{t (T)} (1-3)mentioning

confidence: 99%

Section: ]{T (T)} + [B]{t (T)} (1-3)mentioning

confidence: 99%

Analytical-numerical solution of the inverse problem for the heat conduction equation

Ciałkowski

Maćkiewicz

Kołodziej

et al. 2012

J. Mech. Mater. Struct.

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“…In all these previous studies, the truncated SVD method was applied as a whole domain procedure. Recently, the truncated SVD method has also been applied in a sequential form [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…Gutiérrez et al [19] compare the sequential SVD method with the standard whole domain SVD for one-dimensional and linear problems. The sequential SVD algorithm presents two tunable hyperparameters: the number of future temperature (r) and the rank of the truncated sensitivity matrix (p).…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

García

Cabeza

Rodríguez

2009

International Journal of Thermal Sciences

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Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison

Cabeza

García²,

Rodríguez

2008

Numer Methods Biomed Eng

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Sequential methods that use future times in order to solve an inverse heat conduction problem can be re-formulated as a sequential digital filter algorithm. The aim of this paper is to explore the filter effect of the function specification method and the truncated singular value decomposition method, in a sequential form. For this purpose, the power spectral densities of the corresponding filter coefficients are evaluated and it is shown that they act as band-pass filter. Three numerical tests with different frequency spectra are considered in order to solve a linear one-dimensional transient inverse problem. Furthermore, three models of crescent complexity are used in each method. It is shown that both methods provide similar results and in most cases, the optimum estimations require the same number of future times. As it is expected, similar estimations correspond to a similar band-pass filter. The effect of the number of future times, the influence of the frequency spectrum of the input and the complexity of the model used can be clearly interpreted in the spectral space. The most complex models act as a highly selective band-pass filter, but they require greater number of future times. 555 design problems, for example, the identification of the boundary shape of a domain subject to natural convection from temperature measurements on the other boundary [5]. The IHCP is a clear example of an ill-posed problem [1]. The main difficulty of this type of problem is the instability. From a mathematical point of view, the algebraic formulation of IHCP leads to an ill-conditioned problem, so that a small perturbation in the measured data (due to the unavoidable measurement errors) may cause great oscillations in the estimated function. This difficulty (from a physical point of view) is a consequence of the diffusive nature of heat flow, so that the thermal response at some distance of the boundary is damped and lagged with respect to the active input at the boundary [1]. In order to add stability at the solution of the inverse problem, many and different methods have been reported to solve IHCPs. Among the more versatile methods (applicable to solve multidimensional and non-linear IHCP) the following can be mentioned: Tikhonov regularization [6], iterative regularization [7], mollification [8] and the function specification method (FSM) [1]. The first two methods are considered as 'whole domain' because all the measured temperature data (N ) are used in order to estimate simultaneously all the components of the unknown input. In these methods, the sensitivity matrix can be of great dimensions (N × N ). In contrast, the last two methods are sequential. Therefore, only a small part of the available measurement is used in each step and only one component of the unknown input is estimated at each step. This fact can be an advantage in an online process. A considerable number of contributions have been published considering combinations, modifications and comparisons of the previous methods [9][10][11][12][13][14].Another ...

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A sequential algorithm of inverse heat conduction problems using singular value decomposition

Cited by 49 publications

References 22 publications

Analytical-numerical solution of the inverse problem for the heat conduction equation

Analytical-numerical solution of the inverse problem for the heat conduction equation

Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison

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